Springs provide a restoring force when mechanical work elastically deforms the shape of the spring. The restoring force is directed along a direction that would tend to restore the spring to its relaxed or non-deformed shape or state. Accordingly, springs are often employed in applications that require biasing or restoring the position of an element or structure to a position that corresponds to the spring's relaxed state.
The restoring force is a result of the spring's elastic properties. Namely, when elastically deformed, the spring stores at least a portion of the energy associated with the deforming mechanical work. This mechanical potential provides the restoring force. Springs release the stored potential energy in the form of mechanical work via the restoring force, often resulting in oscillatory motion. Some springs store energy by an elastic elongation/stretching and/or shortening/compression along a longitudinal axis of the spring, such as the case with helical or coil springs.
Within a range of displacement or deformation away from the relaxed state, the magnitude of the restoring force of many springs is approximately linearly proportional with the displacement. Furthermore, the restoring force is directed in the opposite direction of the displacement. Within the linear range of displacement, the restoring force may be modeled by employing Hooke's law. At least to first order, the kinematics of such springs are adequately approximated as harmonic or sinusoidal motion.
When coupled to other structures or elements, harmonic oscillators, such as springs, transmit at least a portion of the vibrational or oscillatory energy to the other structures. Harmonic oscillators and systems comprised of harmonic oscillators resonate at defined resonant frequencies that depend upon properties of the oscillators and the systems. Thus, when a spring is driven at or near a resonant frequency, the transmitted energy may be amplified, causing damage and/or catastrophic failure of the oscillator or the other structures that are receiving the transmitted vibrational energy.
For an oscillating system driven by an energy-carrying signal, the transmissibility of the system is defined as the ratio of the input energy to the transmitted output energy. Because the frequency of the input signal may vary, the transmissibility is often a function of the signal's frequency. Energy-dissipating elements, such as dampers, are often coupled to oscillators to dissipate vibrational energy and decrease the transmissibility of the system. When a damper is coupled to a spring, at least a portion of the energy stored in the spring is transmitted to the damper and dissipated over a time scale much longer than the period of the frequency of the system. Accordingly, the oscillatory motion is at least partially attenuated and/or damped.
However, design requirements of systems and assemblies often constrain the physical placement and types of damping elements that may be employed in various applications. Furthermore, coupling the damping or damper element to the spring may present further engineering challenges. When systems that include a plurality of oscillators require damping, the complexity of the engineering challenges is multiplied. It is for these and other considerations that the following disclosure is provided.